Dynamics and wakes of freely settling and rising cubes

In this investigation, we present numerical simulations of freely settling and rising cubes in a quiescent Newtonian fluid for various values of the Galileo number (70 <= Ga <= 250) and solid-to-fluid density ratio (0.2 <= m <= 7). Ultimately, we obtain a comprehensive two-parameter flow map for a freely moving cube and characterize prominent features of each regime of motion such as trajectories and wake structure. We find that regardless of the density ratio, the cube trajectory transitions from oblique to unsteady vertical, helical and finally random or chaotic. Unlike the case of a sphere, helical motion is observed for all density ratios, marking it as a characteristic type of motion for a cube. Furthermore, we present an in-depth force analysis relevant to the induced lateral motions, and we show that there is a significant jump in the drag coefficient coincident with the onset of the helical regime where large-amplitude lateral displacements appear. We attempt to explain these significant variations of the drag coefficient in connection with the path and vortex structures of the moving cube. Consequently, the enhancement of the drag coefficient is explained to be a combined effect of the vortex-induced drag and the orientation angle of the cube.